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A Case Study Representing Signal Transduction in Liver Cells As a Feedback Control Problem



Systems research has undergone significant changes in recent years due to the inclusion of new applications for control, e.g., microelectronics manufacturing or drug dosage adjustment for biomedical applications, and the use of systems concepts in new areas such as systems biology. As the results from research tend to influence what is taught in a classroom and vice versa, it is very important to have access to illustrative examples that can easily be presented to undergraduate students without requiring an advanced background in the systems area. There are many applications in the field of drug infusion control [1-3] that have been developed and used in classroom example problems. The selection of examples from the field of systems biology, however, is much more limited. This is despite it being widely recognized that feedback loops are common to many cellular functions. [4-8] This paper addresses these points as it investigates a signal transduction pathway involved in the body's response to inflammation or injury, one of many areas of interest to systems biology. While the described system is of interest to the biomedical community, it is simple enough to be presented in an undergraduate class and contains feedback regulation of the signal transduction pathway. Additionally, the system can be appropriately described using block diagrams and transfer function models for perturbations around a steady state. The outline of the paper is as follows: Section 1 is an introduction. Section 2 presents the biological significance of
Vol. 41, No.3, Summer 2007 177
Systems research has undergone signicant changes in
recent years due to the inclusion of new applications for
control—e.g., microelectronics manufacturing or drug
dosage adjustment for biomedical applications—and the use
of systems concepts in new areas such as systems biology.
As the results from research tend to inuence what is taught
in a classroom and vice versa, it is very important to have
access to illustrative examples that can easily be presented
to undergraduate students without requiring an advanced
background in the systems area.
There are many applications in the eld of drug infusion
control[1-3] that have been developed and used in classroom
example problems. The selection of examples from the eld
of systems biology, however, is much more limited. This is
despite it being widely recognized that feedback loops are
common to many cellular functions.[4-8] This paper addresses
these points as it investigates a signal transduction pathway
involved in the body’s response to inammation or injury,
one of many areas of interest to systems biology. While the
described system is of interest to the biomedical community,
it is simple enough to be presented in an undergraduate class
and contains feedback regulation of the signal transduction
pathway. Additionally, the system can be appropriately de-
scribed using block diagrams and transfer function models
for perturbations around a steady state.
The outline of the paper is as follows: Section 1 is an in-
troduction. Section 2 presents the biological signicance of
A Case Study Representing
As a Feedback Control Problem
AbhAy Singh, Arul JAyArAmAn, And Juergen hAhn
Texas A&M University • College Station, TX 77843-3122
ChE classroom
© Copyright ChE Division of ASEE 2007
Abhay Singh is a Ph.D. student at Texas
A&M University, College Station. He re-
ceived his B.E. in chemical engineering
from Panjab University, Chandigarh, India
in 1998. Afterward, he joined Indian Pet-
rochemicals Corporation Ltd. (IPCL) as a
production engineer (Chemical) for four
years. His research interests include sensor
location, soft sensor design, and systems
biology. He is a recipient of the CPC 7 Out-
standing Contributed Paper Award.
Arul Jayaraman received his B.E. (Hons)
in chemical engineering and M.S. (Hons) in
physics from BITS Pilani, India, in 1992, his
M.S. from Tufts University in 1994, and his
Ph.D. from the University of California, Irvine,
in 1998, both in chemical engineering. He
joined Harvard Medical School as instructor
in bioengineering in 2000. He joined Texas
A&M University, College Station, as an assis-
tant professor in 2004. His research interests
include systems biology, molecular bioengi-
neering, and cell-cell communication.
Juergen Hahn received his degree in en-
gineering from RWTH Aachen, Germany,
in 1997, and his M.S. and Ph.D. degrees
in chemical engineering from the University
of Texas, Austin, in 1998 and 2002, respec-
tivel y. He joined Texas A&M Univers ity,
College Station, as an assistant professor
in 2003. His research interests include
process modeling and analysis, systems
biology, and nonlinear model reduction. He
has published more than 30 articles and
book chapters.
Chemical Engineering Education178
the system and describes the model representing the signal
transduction pathway. A block diagram representation of
the signal transduction pathway is developed in Section 3.
Section 4 presents the transfer functions that describe the ef-
fect concentrations of some proteins in the pathway have on
other proteins in the pathway and investigates the dynamic
behavior of the signal transduction pathway. Furthermore,
the dynamics of cells in which the regulatory mechanism
does not function properly, as is often associated with certain
types of cancer,[6] are investigated based upon the developed
transfer function model and compared to the behavior of the
original system. Section 5 presents how this model was used
within an undergraduate process dynamics and control class
taught at Texas A&M University, and Section 6 presents
some conclusions.
Cell signaling refers to the process by which cells sense
their environment, including communication with other cells.
Signaling in cells is initiated by extra-cellular molecules that
activate an intracellular signaling pathway, which ultimately
leads to the formation of proteins involved in basic cellular
processes like regulation of cell growth and division or expres-
sion of other, secreted proteins. This entire process
in which biological information is transferred
from extra-cellular signals into changes
inside a cell is referred to as signal
transduction. As malfunction of sig-
naling pathways can be associated
with some diseases, e.g., certain
types of cancer, cells usually have
regulatory mechanisms built into
signal transduction pathways.
The system under investiga-
tion in this paper deals with
signaling pathways involved
in a body’s response to burn-
injury-induced inflammation.
The injured cells release cyto-
kines, one of which is interleukin
6 (IL-6), to the bloodstream. These
cytokines are sensed by hepatocytes
in the liver, and they activate the acute
phase response (APR). The acute phase
response up- or down-regulates the expres-
sion of certain plasma proteins that take part
in the body’s response to the burn-injury-induced
inammation. Investigating cell signaling in hepatocytes
stimulated by inammatory agents is of crucial importance
to understanding the mechanisms underlying the APR.
The specic topic of this paper is the development of a trans-
fer function model of the JAK (Janus-Associated Kinases)/
STAT (Signal Transducers and Activators of Transcription)
signaling pathway in hepatocytes stimulated by IL-6.[9-10] Sig-
naling through the JAK/STAT pathway is regulated by SOCS3
(Suppressors Of Cytokine Signaling 3) proteins. These pro-
teins are induced by the JAK/STAT signaling pathway once
the signal emanating from the cell surface reaches the nucleus
of the cell. SOCS3 regulates further signaling from the cell
surface to the nucleus of the cell by inhibiting the activation
of STAT3, a process that is usually taking place as a result of
binding of IL-6 to the receptors on the cell surface.
The system under investigation is based upon the JAK/
STAT pathway of the model presented in Singh, et al.,[11] and
is shown in Figure 1. The model of the JAK/STAT pathway
consists of 33 ordinary differential equations, in which each
state corresponds to the concentration of a particular protein
or protein complex in either the cytosol or the nucleus. It is as-
sumed that the cytosol is “well-mixed” and, separately, that the
nucleus can also be viewed as “well-mixed.” The differential
equation for a particular component (A) is written as:
A produced A consumed
= −
∑ ∑
υ υ
, , ( )1
where vA represents the rate of production/consumption of species
A in a particular reaction. It should be noted that these reac-
tions can also include formation and degradation of
a specic protein/protein complex.
While the availability of the detailed
model can have advantages for ana-
lyzing the dynamic concentration
proles of some specic compo-
nents of the system, e.g., dynam-
ics of phosphorylated STAT3
outside of the nucleus, it is not
always required, nor is it neces-
sarily always feasible, to model
every single component of the
system. Instead, it is important
to know the dynamic proles of
certain key components and the
effect a change in the concentra-
tion of one component has on oth-
ers present in the system. This type
of cause-effect relationship can be
conveniently represented in a block dia-
gram. If the relationships between inputs
and outputs can be appropriately described by
linear ordinary differential equations, then transfer
functions can be derived that capture the input-output behav-
ior of the individual components of the system.
These transfer functions are determined by investigating
individual cause-effect relationships in which step inputs are
Figure 1. (above) JAK/STAT signaling pathway induced
by IL-6 in hepatocytes.
Vol. 41, No.3, Summer 2007 179
used to excite the system. It is then possible to derive the transfer function by numerically determining parameters, such that
the difference between the response of the nonlinear model and the transfer function model is minimized.
The following dynamic relationships were identied as important for describing signaling through the JAK/STAT pathway:
c Effect of IL-6 concentration on the receptor complex concentration
c Effect of changes in the concentration of the receptor complex on concentration of STAT3 in the nucleus
c Effect of concentration of nuclear STAT3 on concentration of formed SOCS3
c Effect of concentration of SOCS3 on the receptor complex concentration that can participate in cell signaling
The last of these four dynamic relationships is responsible for the feedback effect in the pathway. An illustration of the block
diagram can be found in Figure 2.
It should be noted that an increase in IL-6 concentration will lead to an increase in receptor complexes that participate in
signaling, and an increase in the number of receptor complexes will also lead to more signaling and a larger amount of nuclear
STAT3. More nuclear STAT3 will lead to increased transcription and translation of the plasma proteins involved in the APR,
while at the same time it leads to the formation of higher levels of SOCS3. SOCS3, on the other hand, has a negative effect on
the activity in the pathway as it prevents phosphorylation of STAT3 by binding to the receptor complexes.
The concentration of IL-6 is used as the input for the system and the concentration of nuclear STAT3 is used as the output of the model.
In order to identify the transfer functions, the cell is assumed to be at steady state with a constant input of 3.0E-4 nM of IL-6,
resulting in a concentration of the phosphorylated receptor complex (IL6-gp80-gp130-JAK*)2 of 6.973E-4 nM, a concentra-
tion of SOCS3 of 0.1047 nM, and a concentration the nuclear STAT3 dimer (STAT3N*-STAT3N*) of 0.1048 nM. The cell is
perturbed from the steady-state by a step change of ±10% in the concentration of IL-6, which serves as the input to the system.
The obtained output trajectories are used for identication of the following transfer functions:
IL s
6 80 130
5 45
1 65 1
=− −
( )
− −
( )
3 3
6 80 130
* *
. .
0 03462 0 4462 1
s S
+ +
=33 1 08 1
6 80 130
0 6
=− −
( )
0 0019
1 2 1
Figure 2. Block diagram representation of signaling pathway implemented in Simulink.
Chemical Engineering Education180
A comparison of the response of the original nonlinear
system and the one obtained from the transfer function model
is shown in Figures 3, 4, and 5. It can be concluded that the
linear transfer function model can adequately represent the
behavior of the original (nonlinear) system. It should be noted
that this rst set of simulation experiments was performed
for the sole reason of determining the quality of the t of the
transfer function models to the response generated by the
nonlinear system. It is also important to keep in mind that
the linear approximation, resulting from the use of transfer
functions, will only be able to represent the original nonlinear
system for excitations near the conditions for which the linear
model was derived.
A second experiment was run using the identied transfer
function model. For these simulations, it was assumed that
the effect of SOCS3 on the phosphorylation of STAT3 had
been removed from the cell, as shown in Figure 6, and in the
block diagram, shown in Figure 7. This effect is similar to a
SOCS3 knockout cell where SOCS3 is not produced, which
has medical signicance associated with certain types of
cancers. The only difference between a SOCS3 knockout cell
and the behavior simulated here is that the feedback part is cut
open after the formation of SOCS3 instead of before.
It can be observed from Figure 8 and Figure 9 that the
signal is not down-regulated due to the absence of the effect
of SOCS3 on the system. The receptor complex (IL6-gp80-
gp130-JAK*)2 (Figure 8) and the nuclear STAT3 dimer
Figure 3. Dynamic response of (IL6-gp80-gp130-JAK*)2
complex for ±10% step change in the IL-6 concentration
around the steady state (0.5 pM IL-6 concentration).
Figure 4. Dynamic response of STAT3N*-STAT3N*
complex for ±10% step change in the IL-6 concentration
Figure 5. Dynamic response of SOCS3 for ±10% step
change in the IL-6 concentration about the steady state
(0.5 pM IL-6 concentration).
Figure 6. JAK/STAT signaling pathway induced by IL-6
in cells where the effect of SOCS3 on phosphorylation of
STAT3 has been removed.
Vol. 41, No.3, Summer 2007 181
m Figure 7. (above) Block diagram of the “open-loop”
signaling pathway implemented in Simulink.
b Figure 8. (left) Dynamic response of (IL6-gp80-gp130-
JAK*)2 complex for ±10% step change in the IL-6 concen-
tration around the steady state (0.5 pM IL-6 concentra-
tion) in SOCS3 knockout cells.
. Figure 9. (below, left) Dynamic response of STAT3N*-
STAT3N* for ±10% step change in the IL-6 concentration
around the steady state (0.5 pM IL-6 concentration) in
SOCS3 knockout cells.
(STAT3N*-STAT3N*) (Figure 9) show a larger deviation
from the steady-state value when compared to the closed-
loop responses shown in Figures 3 and 4. Moreover, the
comparable open-loop response from the nonlinear and the
transfer functions indicate that cell behavior can, locally, be
adequately described by the transfer function model.
The presented model has been used at several points
throughout the Process Dynamics and Control course taught
in the chemical engineering department at Texas A&M
1) It is used during the rst week of the semesters when
different systems that include feedback control are
introduced to make the students aware of how often they
come in contact with such systems.
2) The model is revisited when the material about deriv-
ing linear transfer functions from data is covered. In
this specic case the data is generated by the original
Chemical Engineering Education182
nonlinear model whereas the linear transfer functions
represent the model to be t to this data.
3) Since the model contains negative feedback regula-
tion, it is also used when the effect of negative feedback
control on a system is discussed.
Using the same example throughout the semester allows
students to participate in several steps of modeling and model
validation, rather than just performing individual tasks. Also,
this model describing a signal transduction pathway is used
alongside models teaching traditional chemical engineering
This paper presented a case study in which a signal transduc-
tion pathway was represented as a block diagram, and linear
transfer function models were identied in individual blocks
for perturbations of the model around a steady state.
The system behavior was broken up into four components,
and each part represented the effect a change in the concen-
tration of one component has on others present in the signal
transduction pathway. This was illustrated in how SOCS3
serves as an inhibitor of the signal transduction pathway,
and how the effect SOCS3 has on the signaling activity can
be appropriately described by negative feedback in the block
diagram representation of the system.
Also shown was how the identied model correctly repre-
sented the behavior of the original system for the three key
components chosen. Simulation studies have been performed
on SOCS3 knockout cells, which can be compared to the
“open-loop” behavior of the system, as there is no effect of
SOCS3 on the signal transduction pathway. It was found that
our identied model appropriately described the behavior of
the SOCS3 knockout cell in this way.
The presented case study can serve as an example for il-
lustrating feedback regulation in cell signaling for process
control education.
The authors gratefully acknowledge partial nancial sup-
port from the ACS Petroleum Research Fund (Grant PRF#
43229-G9) and from the National Science Foundation (Grant
CBET# 0706792).
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... Research on the molecular mechanisms of signal transduction is a very important topic that has attracted significant interest from biologists, bioengineers and biotechnologists [4], [5], [6], [7]. Although considerable progress in the identification of the molecular components involved in cell functions has been made over the past decades, the resulting dynamic models are highly complex and it is not possible to substantiate if each aspect of the model is correct. ...
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This paper introduces the application of linear multivariate statistical techniques, including partial least squares (PLS), canonical correlation analysis (CCA) and reduced rank regression (RRR), into the area of Systems Biology. This new approach aims to extract the important proteins embedded in complex signal transduction pathway models. The analysis is performed on a model of intracellular signalling along the janus-associated kinases/signal transducers and transcription factors (JAK/STAT) and mitogen activated protein kinases (MAPK) signal transduction pathways in interleukin-6 (IL6) stimulated hepatocytes, which produce signal transducer and activator of transcription factor 3 (STAT3). A region of redundancy within the MAPK pathway that does not affect the STAT3 transcription was identified using CCA. This is the core finding of this analysis and cannot be obtained by inspecting the model by eye. In addition, RRR was found to isolate terms that do not significantly contribute to changes in protein concentrations, while the application of PLS does not provide such a detailed picture by virtue of its construction. This analysis has a similar objective to conventional model reduction techniques with the advantage of maintaining the meaning of the states prior to and after the reduction process. A significant model reduction is performed, with a marginal loss in accuracy, offering a more concise model while maintaining the main influencing factors on the STAT3 transcription. The findings offer a deeper understanding of the reaction terms involved, confirm the relevance of several proteins to the production of Acute Phase Proteins and complement existing findings regarding cross-talk between the two signalling pathways. Copyright
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This paper analyses the sodium nitroprusside infusion rate control problem that occurs in patients after surgery. The process includes several parameters that can vary over a significant range. Analysis of the model parameters has shown that an internal model controller (IMC) that can meet robust stability and performance criteria can be designed for variations in all of the parameters but one. This model parameter is found from an adaptation law that is introduced in this paper. The resulting controller was shown to meet the robust performance criteria for several simulated patients including some that showed extreme reactions to the drug infusion.
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The family of cytokines signalling through the common receptor subunit gp130 comprises interleukin (IL)-6, IL-11, leukaemia inhibitory factor, oncostatin M, ciliary neurotrophic factor and cardiotrophin-1. These so-called IL-6-type cytokines play an important role in the regulation of complex cellular processes such as gene activation, proliferation and differentiation. The current knowledge on the signal-transduction mechanisms of these cytokines from the plasma membrane to the nucleus is reviewed. In particular, we focus on the assembly of receptor complexes after ligand binding, the activation of receptor-associated kinases of the Janus family, and the recruitment and phosphorylation of transcription factors of the STAT family, which dimerize, translocate to the nucleus, and bind to enhancer elements of respective target genes leading to transcriptional activation. The important players in the signalling pathway, namely the cytokines and the receptor components, the Janus kinases Jak1, Jak2 and Tyk2, the signal transducers and activators of transcription STAT1 and STAT3 and the tyrosine phosphatase SHP2 [SH2 (Src homology 2) domain-containing tyrosine phosphatase] are introduced and their structural/functional properties are discussed. Furthermore, we review various mechanisms involved in the termination of the IL-6-type cytokine signalling, namely the action of tyrosine phosphatases, proteasome, Jak kinase inhibitors SOCS (suppressor of cytokine signalling), protein inhibitors of activated STATs (PIAS), and internalization of the cytokine receptors via gp130. Although all IL-6-type cytokines signal through the gp130/Jak/STAT pathway, the comparison of their physiological properties shows that they elicit not only similar, but also distinct, biological responses. This is reflected in the different phenotypes of IL-6-type-cytokine knock-out animals.
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Experimental studies of two control methodologies for regulating multiple variables in critical care patients are described. The control strategies for the regulation of mean arterial pressure and cardiac output use vasoactive and inotropic drugs. Corresponding experimental results from the evaluation of the controllers with canines are presented.
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The IL (interleukin)-6-type cytokines IL-6, IL-11, LIF (leukaemia inhibitory factor), OSM (oncostatin M), ciliary neurotrophic factor, cardiotrophin-1 and cardiotrophin-like cytokine are an important family of mediators involved in the regulation of the acute-phase response to injury and infection. Besides their functions in inflammation and the immune response, these cytokines play also a crucial role in haematopoiesis, liver and neuronal regeneration, embryonal development and fertility. Dysregulation of IL-6-type cytokine signalling contributes to the onset and maintenance of several diseases, such as rheumatoid arthritis, inflammatory bowel disease, osteoporosis, multiple sclerosis and various types of cancer (e.g. multiple myeloma and prostate cancer). IL-6-type cytokines exert their action via the signal transducers gp (glycoprotein) 130, LIF receptor and OSM receptor leading to the activation of the JAK/STAT (Janus kinase/signal transducer and activator of transcription) and MAPK (mitogen-activated protein kinase) cascades. This review focuses on recent progress in the understanding of the molecular mechanisms of IL-6-type cytokine signal transduction. Emphasis is put on the termination and modulation of the JAK/STAT signalling pathway mediated by tyrosine phosphatases, the SOCS (suppressor of cytokine signalling) feedback inhibitors and PIAS (protein inhibitor of activated STAT) proteins. Also the cross-talk between the JAK/STAT pathway with other signalling cascades is discussed.
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Cytokines like interleukin-6 (IL-6) play an important role in triggering the acute phase response of the body to injury or inflammation. Signaling by IL-6 involves two pathways: Janus-associated kinases (JAK) and signal transducers and activators of transcription (STAT 3) are activated in the first pathway while the second pathway involves the activation of mitogen-activated protein kinases (MAPK). While it is recognized that both pathways play a major role in IL-6 signal transduction, a majority of studies have focused on signaling through either one of the pathways. However, simultaneous signaling through both JAK/STAT and MAPK pathways is still poorly understood. In this work, a mathematical model has been developed that integrates signaling through both the JAK/STAT and the MAPK pathway. The presented model is used to analyze the effect of three molecules that are involved in the regulation of IL-6 signaling-SHP-2 (domain containing tyrosine phosphatase 2), SOCS3 (suppressor of cytokine signaling 3), and a STAT3 nuclear phosphatase (PP2)-on the dynamics of IL-6 signal transduction in hepatocytes. The obtained results suggest that interactions between SHP-2 and SOCS3 influence signaling through the JAK/STAT and the MAPK pathways. It is shown that SHP-2 and SOCS3 do not just regulate the pathway that they are known to be associated with, (SHP-2 with MAPK and SOCS3 with JAK/STAT), but also have a strong effect on the other pathway. Several simulations with SOCS3, SHP-2, and PP2 knockout cells, that is, where the signaling pathway is unable to produce these proteins, have been performed to characterize the effect of these regulatory proteins on IL-6 signal transduction in hepatocytes.
Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.
Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem.1999, 274, 27119−27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can “back-propagate” effects upstream of the target, specifically resulting in increased steady-state upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated.
Many distinct signaling pathways allow the cell to receive, process, and respond to information. Often, components of different pathways interact, resulting in signaling networks. Biochemical signaling networks were constructed with experimentally obtained constants and analyzed by computational methods to understand their role in complex biological processes. These networks exhibit emergent properties such as integration of signals across multiple time scales, generation of distinct outputs depending on input strength and duration, and self-sustaining feedback loops. Feedback can result in bistable behavior with discrete steady-state activities, well-defined input thresholds for transition between states and prolonged signal output, and signal modulation in response to transient stimuli. These properties of signaling networks raise the possibility that information for “learned behavior” of biological systems may be stored within intracellular biochemical reactions that comprise signaling pathways.
The intercellular communication that regulates cell fate during animal development must be precisely controlled to avoid dangerous errors. How is this achieved? Recent work has highlighted the importance of positive and negative feedback loops in the dynamic regulation of developmental signalling. These feedback interactions can impart precision, robustness and versatility to intercellular signals. Feedback failure can cause disease.
The development of control-relevant models for a variety of biomedical engineering drug delivery problems is reviewed in this paper. A summary of each control problem is followed by a review of relevant patient models from literature, an examination of the control approaches taken to solve the problem, and a discussion of the control-relevance of the models used in each case. The areas examined are regulating the depth of anesthesia, blood pressure control, optimal cancer chemotherapy, regulation of cardiac assist devices, and insulin delivery to diabetic patients.